Have some questions about reasoning in following answer indicating problems with compatibility of hypothetical discretizing specetime with known observations.
L. Motl argued there:
A discrete spacetime immediately implies lots of bulk degrees of freedom that remember the detailed arrangement of the discrete blocks - unless it is regular and unique. Consequently, the "vacuum" carries a gigantic entropy density - the Planck entropy density if the concept is applied at the Planck scale. [...]
Questions:
(1) Could somebody elaborate the idea & intuitive picture why in case we assume spacetime to be discrete we get as inevitable consequence the presence of "lots of bulk degrees of freedom" remember the detailed arrangement of the discrete blocks?
Going maybe one step back, here appears the term "bulk degrees of freedom", about its exact meaning in this context I'm not completely sure.
So intermediate question to avoid confusions: What is meant in this context by "bulk" precisely? A guess: that one from M-theory?
Or is here by "bulk" refered in informal sense synonymously just to huge amount of abstact informations?
Assuming the first, why then putative discreteness of spacetime would force that the dimension of the whole bulk space - so in that sense the "total" dimension of such a "model manifold" emdedding spacetime as its hypersurface (or approp intersection of hypersurfaces) - would tend to be "big"?
(2) Furthermore is claimed that that the only way to avoid this scenario is that such putative discrete spacetime is "regular and unique". Could somebody clarify what is precisely in this context meant by "regularity" and "uniqueness"?
My guesses: On "regularity" I conjecture this referes to that all such minimal "elementary block units" are taken to be identical in sense of lattice theory, namely that we model the discrete spacetime as union of "atomic blocks" (where "atomic in sense of not further divisible in smaller parts) "nested" in a fixed lattice $L \cong \Bbb Z^4 \subset \Bbb R \times \Bbb R^3$ between points and "walls" of the lattice. Especially, it cannot happen that two "atomic blocks" have different "shape". Is that to what is refered by "regualarity" above?
And idea concerning "uniqueness": Doesn't this just refer to that after fixing such a lattice - regarded as a reference frame in physical terms -there exist no nontrivial Lorentz trafo which not changes the "shape" of elementary cell of the lattice? Therefore this lattice/frame is in that sense "prefered", as any nontrivial Lorentz trafo would map it to different lattice where the physics would be different due to change of shape?
PS 1: I'm asking as a mathematician trying to develop "right" intuition for the quoted answer, so maybe some points would appear to a trained physicist "trivial".
PS 2: Asked previously question about more aspects of the quoted answer but the question got closed due to amount of questions and thus missing focus. So tried here here to left some out which will maybe posted later.
